The present invention relates to ellipsometers, and more particularly to rotating compensator ellipsometers.
Optical ellipsometry has long been recognized as providing accurate characterizations of semiconductors and other materials, their surface conditions, layer compositions and thicknesses, and for characterizing overlying oxide layers. This non-destructive technique is particularly needed to evaluate thickness, crystallinity, composition and index of refraction characteristics of thin films deposited on semiconductor or metal substrates to ensure high yields during fabrication.
An ellipsometer probes a sample with a light beam having a known polarization state. The light beam is reflected at a non-normal incidence from the surface of the sample. The polarization state of the beam is modified upon reflection in a way that depends upon the structure of the sample. By accurately measuring the polarization state of the reflected beam and comparing it to the original polarization state, various properties of the sample can be ascertained.
In spectroscopic ellipsometry, the probing wavelength is changed and the ellipsometric measurement is repeated at each new wavelength. Spectroscopic ellipsometry is ideal for multi-material samples formed in stacked layers. The different depth penetrations and spectral responses that vary depending upon the material and wavelength of light provide additional information about a sample that is not available using single wavelength ellipsometers.
One possible ellipsometric configuration uses the following components: 1) a light source, 2) a linear polarizer (xe2x80x9cpolarizerxe2x80x9d), 3) the sample (to be analyzed), 4) a second linear polarizer (xe2x80x9canalyzerxe2x80x9d), and 5) a detector. The polarizer produces totally polarized light, and the analyzer assesses the polarization state of the beam after reflection from the sample. Either the polarizer or the analyzer is rotated so that the detector signal can be used to accurately measure the linear polarization component of the reflected beam. Then, the circularly polarized component is inferred by assuming that the beam is totally polarized, and what isn""t linearly polarized must be circularly polarized.
An advantage of this type of ellipsometer is that the polarizer and analyzer can function over a wide range of wavelengths, thus providing a broad perspective of the sample as compared to measurements made at a single wavelength. A common method of spectroscopic ellipsometry is to use a broadband light source, such as a Xe arc lamp, with data acquisition occurring in a serial or parallel mode. In the serial mode, a monochrometer is placed before the detector to filter out all wavelengths except for the desired probe wavelength. Multi-wavelength measurements are performed serially, one wavelength at a time, by properly adjusting the monochrometer for each measurement. In parallel operation, a polychromatic light beam having a broad range of wavelengths is directed to the sample. The reflected beam is diffracted to a photodetector array or an optical multichannel analyzer by a diffraction grating or a prism. The multi-wavelength measurements are performed in parallel, with all wavelengths of interest being measured at the same time.
Such an ellipsometer, commonly called a rotating-polarizer or rotating-analyzer ellipsometer, is termed xe2x80x9can incompletexe2x80x9d polarimeter, because it is insensitive to the handedness of the circularly polarized component and exhibits poor performance when the light being analyzed is either nearly completely linearly polarized or possesses a depolarized component.
The latter limitations of the rotating-polarizer and rotating-analyzer ellipsometers can be overcome by including a rotating compensator placed between the polarizer and the analyzer (both of which are fixed and not rotating) that rotates about the propagating axis of the beam. The compensator can be placed either between the sample and the polarizer, or between the sample and the analyzer. Such a configuration is commonly called a rotating compensator ellipsometer. The compensator is an optical component that delays the light polarized parallel to its slow axis relative to light polarized parallel to its fast axis by an amount proportional to the refractive index difference along the two directions and the thickness of the plate, and inversely proportional to the wavelength of the light.
It is known in the art that the intensity I of a beam transmitted through an ideal compensator-analyzer combination is expressed as:
I[|Ex|2+|Ey|2]=Io[|Ex|2(cos2(xcex4/2)+(xc2xd)sin2(xcex4/2))xe2x80x83xe2x80x83(1)
+|Ey|2(xc2xd)sin2(xcex4/2)
+(|Ex|2xe2x88x92|Ey|2)(xc2xd)sin2(xcex4/2)cos(4C)
+Re(ExEy*)sin2(xcex4/2)sin(4C)
xe2x88x92Im(ExEy*)sinxcex4sin(2C)],
where Io is the intensity of the incoming beam, Ex and Ey are the projections of the incident electric field vector parallel and perpendicular, respectively, to the transmission axis of the analyzer, xcex4 is the phase retardation of the compensator, C is the azimuth (rotational) angle of the fast (reference) axis of the compensator also relative to the transmission axis of the analyzer. In the case of a continuously rotating compensator, C=xcfx89t, where xcfx89 is the angular rotational frequency of the compensator.
As can be seen by Eqn. (1), a rotating compensator will generate a signal having a dc component, a 2xcfx89 (two omega) component and a 4xcfx89 (four omega) component with respect to the rotation rate of the compensator. While usable information is generated from both the two omega and four omega signals, it is often felt that the two omega signal is the most significant for analysis. The two omega component is maximized when the phase retardation of the compensator is 90xc2x0 (i.e. sinxcex4=1), and disappears at phase retardations of 0xc2x0 and 180xc2x0 (sinxcex4=0). Since the phase retardation of the compensator is a function of wavelength, this system lends itself to single wavelength operation only, or to a range where the wavelength changes only by a relatively small amount from the center wavelength of the compensator. As the wavelength deviates from the center wavelength such that the amount of phase retardation induced by the compensator deviates from 90 degrees, the relative intensity of the two omega signal is reduced. Therefore, multiple wavelength operation of rotating compensator ellipsometers has traditionally been limited to relatively narrow wavelength ranges (less than a factor of two in wavelength) corresponding to substantially 90 degree phase retardations induced by the compensator.
There is a need for a rotating compensator ellipsometer system that simultaneously obtains data over a wide range of wavelengths, which necessarily corresponds to phase retardations that vary significantly from the optimal 90xc2x0.
One prior-art solution to expand the effective wavelength range of retardation-based ellipsometers is to replace the rotating compensator with a photoelastic modulator. The phase retardation of the photoelastic modulator is a function of both the wavelength and the drive voltage to the modulator. During ellipsometric measurements, a series of wavelengths within the wavelength range of interest are sequentially scanned while the drive voltage to the photoelastic modulator is simultaneously changed. The change in drive voltage tracks the change in wavelength such that the phase retardation of the modulator is maintained at approximately 90xc2x0 when each wavelength is measured to maximize the two omega signal. The drawback of such a spectroscopic ellipsometer is that the wavelengths are scanned sequentially, and not in parallel, which results in a reduced signal-to-noise ratio for the same scan time. Also, such modulators operate at frequencies (for example 50 KHz) that are too high for photodiode array detectors to follow.
Another prior-art solution is to use a quasiachromatic wave plate for which the retardation is relatively invariant for a finite wavelength range. Such plates, often called Pancharatnam plates, are commonly used in astronomy as reviewed by K. Serkowski in the compendium Planets, Stars, and Nebulae studied with Photopolarimetry, ed. T. Gehrels (University of Arizona Press, Tucson, 1974), pp. 135-174. One polarimeter of a half-wave design is discussed in a paper by D. Clarke and R. N. Ibbett, J. Sci. Inst. Series 2, 1, 409-412 (1968), who used a fixed mica half-wave plate to test a concept but warned on p. 410 that xe2x80x9cA simple half-wave plate is useful over a range of about 300 xc3x85. For extended wavelength ranges an achromatic half-wave plate must be considered.xe2x80x9d
Numerous configurations involving quarter-wave and half-wave retarders, in some cases combined to form quasiachromatic quarter- and half-wave plates, have been reviewed by Serkowski in the above mentioned volume. Other discussions can be found in the book Polarized Light and Optical Measurement by D. Clarke and J. F. Grainger (Pergamon, Oxford, 1971). In the configurations listed, the quarter-wave plates are used for quarter-wave retardation and the half-wave plates for half-wave retardation. As discussed in the article by Serkowski, it is possible to combine retarders that exhibit quarter- and half-wavelength retardation at a specific wavelength to achieve quasiachromatic quarter- or half-wavelength retardation behavior over a range of wavelengths However, the usable range for a triple (Pancharatnam) stack of such plates does not exceed a factor of 2, and a 6-fold (Serkowski) stack of such plates does not exceed a factor of about 3. Further, these stacks are intrinsically complex and very difficult to align (and to maintain such alignment). In addition, the azimuth angles of the principle axes of these stacks are not fixed with respect to the elements but vary with wavelength. None of these references contemplate a wide-bandwidth instrument using a single quarter-wave retarder over a wide range of wavelengths that includes half-wave retardation.
There is a need for a spectroscopic ellipsometer that operates with parallel detection over a relatively broad wavelength range (on the order of at least a factor of four) such that useful information can be simultaneously obtained throughout the entire wavelength range.
It has been discovered by the present inventors that a sample can be analyzed with good accuracy if information obtained from both the two omega and four omega components of the rotating compensator spectroscopic ellipsometer signal are combined. In particular, this allows spectroscopic ellipsometric analysis to be performed over very large ranges of wavelengths, as long as both the two omega and four omega signals are utilized and at least one of the signals is present at every wavelength measured. The broadband spectroscopic ellipsometer of the present invention simultaneously measures at wavelengths of light within a broad wavelength range of interest, where the measurement wavelengths measured correspond to compensator phase retardations that are sufficiently near 180xc2x0 and sufficiently near at least 90xc2x0 or 270xc2x0.
The ellipsometer of the present invention includes a light generator that generates a beam of polychromatic light having a range of wavelengths and a known polarization for interacting with the sample. A compensator is disposed in the path of the light beam to induce phase retardations of the polarization state of the light beam. The range of wavelengths and the compensator are selected such that at least a first effective phase retardation value is induced that is within a primary range of effective retardations of substantially 135xc2x0 to 225xc2x0, and at least a second effective phase retardation value is induced that is outside of that primary range. The compensator is rotatable about an axis substantially parallel to the propagation direction of the light beam. An analyzer interacts with the light beam after the light beam interacts with the sample. A detector measures intensity of the light after the interaction with the analyzer as a function of the rotational angle of the compensator and of wavelength, including light intensities of those wavelengths corresponding to the first and second effective phase retardation values. These intensities can be analyzed for the polarization state of the light incident on the analyzer.
The method of analyzing a sample using the ellipsometer of the present invention includes generating a beam of polychromatic light having a range of wavelengths and a known polarization for interacting with the sample. Phase retardations of a polarization state of the light beam are induced with a compensator by selecting the range of wavelengths and the compensator such that at least a first effective phase retardation value is induced that is within a primary range of effective phase retardations of substantially 135xc2x0 to 225xc2x0, and at least a second effective phase retardation value is induced that is outside of that primary range. The compensator is rotated about an axis substantially parallel to the propagation direction of the light beam. The light beam is subjected to interaction with an analyzer after the beam interacts with the sample. The intensity of the light is measured after the interaction with the analyzer as a function of the rotational angle of the compensator and of wavelength, including light intensities of those wavelengths corresponding to the first and second effective phase retardation values. These intensities correspond to the polarization state of the light impinging on the analyzer.
Other aspects and features of the present invention will become apparent by a review of the specification, claims and appended figures.